Method and apparatus to increase the resolution and widen the range of differential mobility analyzers (DMAs)

ABSTRACT

A differential mobility analyzer (DMA) for separating charged particles or ions suspended in a gas and a method of using the DMA for separating such particles. The invention includes various means for increasing the resolution of the DMA by stabilizing the laminar flow within the DMA and by allowing unusually large flow velocities.

CROSS REFERENCE TO RELATED APPLICATION

[0001] This application claims the benefit of priority to U.S.Provisional Patent Application No. 60/324,143, filed on Nov. 2, 2001.

FIELD OF THE INVENTION

[0002] The invention relates to a method and apparatus for sizing andclassifying charged particle or ions in a differential mobilityanalyzer.

BACKGROUND OF THE INVENTION

[0003] Differential mobility analyzers (DMAs) are the most powerfulinstruments available for sizing and classifying particles, especiallyin the diameter range below 100 nanometers. The most common DMA designinvolves two concentric cylindrical electrodes. The commercial versionsof various instruments have served rather well the aerosol community'sfor several decades. A number of cylindrical designs have been studied,with different ratios between the electrode radii R₁ and R₂ and theaxial distance L between inlet and outer slits for the aerosol flow.Other geometrical variations upstream the inlet or downstream the outletslits have been tested for special purposes such as reducing theparticle losses or the pressure drop, or for improving flow laminarityat moderate Reynolds number or to reach unusually high Reynolds numbers.As is well known to those skilled in the art, the Reynolds number is adimensionless number which is equal to the density of a fluid times itsvelocity times a characteristic length, divided by the fluid's viscositycoefficient.

[0004] DMAs are used to separate small charged particles suspended in agas according to their electrical mobility Z. They combine particle-freefluid flow (the sheath gas) and electric fields to drive chargedparticles introduced through a first narrow slit (the inlet or injectionslit) located in a first electrode into a second narrow slit located ina second electrode. The space between these two slits and electrodeswill be referred to as the “working section” of the DMA. Ideally, amongthe particles introduced through the injection slit, only those withmobilities contained within a relatively small range ΔZ centered about amean value Z are sampled through the outlet slit. The inverse of theratio ΔZ/Z is a measure of the DMA resolution. Traditionally, DMAs havebeen used for the separation of particles considerably larger than 5nanometers. However, developments over the last decade have made theseinstruments suitable also for the separation of particles a fewnanometers in diameter, and even smaller ions. Their use in the analysisof suspended ions and macroions is therefore of considerable practicalinterest. Such applications would benefit from the development ofinstruments of higher resolution and wider range than those that havebeen traditionally available. It should be noted that the term ion, asused in the instant application, refers not only to molecular ions, butalso to charged clusters and in general to any charged particle.

[0005] The main obstacle limiting DMA resolution in the nanometerdiameter range is Brownian motion. It is known that the associated peakbroadening can be reduced considerably by two different means: (a) ageometrical design taking advantage of the existence of an optimalrelative positioning between the two slits, and (b) increasing theReynolds number (Re) of laminar operation of the sheath gas flow in theDMA to values as large as possible. Rosell-Llompart et al., Minimizationof the diffusive broadening of ultrafine particles in differentialmobility analyzers, in Synthesis and Characterization of UltrafineParticles, pp. 109-114 (1993), the subject matter of which is hereinincorporated by reference in its entirety, discloses high Reynoldsnumber formulation accounting only for Brownian diffusion broadening incylindrical DMAs. The relative full width ΔZ/Z of the mobility peakassociated to particles of fixed mobility Z can be written as

(ΔZ/Z)²=161n2 D/(L*U) (b+1/b);   (1)

b=L/L*; L* ²=(R ₂ ² −R ₁ ²)²/[2(R ₂ ² +R ₁ ²)].   (2,3)

[0006] D is the diffusivity of the particles, related to theirelectrical mobility Z via

Z=De/(kT),   (4)

[0007] where e is the elementary charge (the particles are taken to besingly charged), k Boltzmann's constant and T the absolute temperature.R₁ and R₂ are the radii of the inner and outer cylindrical electrodes. Lis the axial distance between the inlet and outlet slits, and U is thefluid velocity, taken to be independent of the radial coordinate r (plugflow). Suitable generalizations exist of these results for othervelocity profiles, plane geometries, and even converging two-dimensionalor axisymmetric situations. But equations (1-3) are representative ofsuch broader cases, and suffice for the purposes of the presentdiscussion. Since (b+1/b)≧2, it is clear that, at given radii R₁ and R₂and fixed speed U, the resolution is maximized when the length L isequal to L*. The advantages of using DMAs of near-optimal length werefirst demonstrated experimentally by Rosell-Llompart et al. (1993).

[0008] The need to use very high Reynolds numbers follows alsoimmediately from (1). L* coincides with the width Δ=R₂−R₁ of the workingsection in the limit of a small gap, Δ<<R₂ (when R₁ tends to R₂), and isreasonably close to it even if R₁/R₂ differs substantially from unity(L*/Δ=0.843 when R₁/R₂=0.222). Hence, the ratio D/(L*U) is fairly closeto the Peclet number defined here as

Pe=D/(ΔU).

[0009] For the purposes of separating efficiently small speciesaccording to their mobility, it is desirable that ΔZ/Z be as small as1%, even for ions with diameters as small as 1 or 2 nanometers. Since(b+1/b)≧2, this requirement implies that L*U/D>2.22×10⁵. Note also thatsmall ions in standard air have mobilities of 2 cm²/V/s, with associateddiffusivities D=0.05 cm²/s. The dimensionless ratio between thekinematic viscosity of air ν (=0.15 cm²/s) and D is therefore ν/D=3, andthe quantity UL*/ν (close to the Reynolds number Re=UΔ/ν) needs then tobe as high as 0.74×10⁵. We shall see that, in order to cover a widerange of particle sizes, it is convenient to use DMAs with a distance Lbetween the inlet and outlet slits as large as 3L* or even larger (b>3),in which case the resolution is reduced by a factor [(b+1/b)/2]^(1/2).To compensate for this effect calls for Reynolds numbers (Re) in excessof 10⁵.

[0010] The need for high Reynolds (or Peclet) numbers to moderatediffusion in convective diffusive flows is well known. However, thepractical exploitation of this knowledge is made difficult by thenatural tendency of high Reynolds number flows to become turbulent, aswell as by the difficulties associated to the generation of the ratherlarge flows required. For instance, Rosell, J., I. G. Loscertales D.Bingham and J. Fernández de la Mora “Sizing nanoparticles and ions witha short differential mobility analyzer”, J. Aerosol Science, 27 695-719,1996., have demonstrated an ability to reach Reynolds numbers as largeas 5000 in a variant of the widely used DMA disclosed by Winklmair, etal., A New Electro-mobility Spectrometer for the Measurement of AerosolSize Distributions in the Size Range from 1 to 1,000 nanometers, J.Aersol Sci., Vol. 22, pp. 289-296 (1991), (commonly referred to as the“Vienna DMA”). But they needed flow rates of some 800 liters/minute,with associated pressure drops close to half an atmosphere. Under suchconditions it would have been rather difficult to attain the desiredrange of Reynolds numbers up to 10⁵.

[0011] Some important aspects of the problem of achieving high Reynoldsnumbers, while avoiding turbulent transition, have been addressed inU.S. Pat. No. 5,869,831 and U.S. Pat. No. 5,936,242, both to de la Mora,et al., the subject matter of which are herein incorporated by referencein their entirety, following the method of greatly reducing the level ofperturbations in the inlet sheath gas flow by means of several stages oflaminarizing screens and filters followed by a large contraction whichaccelerates substantially the sheath gas prior to the working section.For brevity, this large inlet contraction will be referred to as the“trumpet”, even in non-axisymmetric designs.

[0012] Some additional clarifications are required here on the variousmeans available to delay transition to relatively high Reynolds numbers.It is well known that fully developed parabolic flow inside a tube tendsto become turbulent at a critical Reynolds number near 2000, and thatthis critical value can be increased greatly when the inlet flow iscarefully freed from velocity fluctuations. Often, the velocity profileat the entry of the working section is far closer to flat thanparabolic, and this profile is less unstable than the parabolic flow.Still, the boundary layers forming near the cylindrical electrode wallstend also to become turbulent, and the critical conditions at which thishappens are also pushed to considerably larger Reynolds numbers by ahighly laminar inlet flow. Even so, transition eventually occurs.Furthermore, even in the most carefully prepared laminarizing system, itis very difficult to avoid all external sources of velocityfluctuations. And even when the fluctuation level of the entering flowis very small, local perturbations will tend to appear in the unstablemixing layer following the aerosol inlet. This last difficulty isaddressed in the Vienna DMA by a slight reduction in the DMA crosssection immediately after the inlet slit, which tends to stabilize theflow. However, this feature is meant to stabilize flows at Reynoldsnumbers well below 2000, and is likely to be ineffective at Re=10⁵. Arecent study of a variant of the Vienna DMA supplied with the very largeinlet trumpet introduced in U.S. Pat. No. 5,869,831 observes turbulenttransition at Re near 35,000. The boundary layers over their cylindricalelectrodes evolve nearly as that over a flat plate, for which comparableconditions for transition are observed in an incoming stream with avelocity fluctuation level of the order of 1%. In contrast, free streamturbulence levels some 100 times smaller are required to achievecritical Reynolds numbers in the range 10⁵-10⁶ in non-converginggeometries. These observations indicate that, in planar or cylindricalDMAs, neither the large trumpet inlet proposed in U.S. Pat. No.5,869,831, nor the slight acceleration used following the inlet slit ofthe Vienna DMA suffice to create laminar flows in the desired range Re10⁵.

SUMMARY OF THE INVENTION

[0013] The present invention comprises a method and apparatus forseparating charged particles or ions in a differential mobilityanalyzer, wherein a stream of charged particles or ions is introducedinto an upstream portion of an analyzing region through an inlet slit,and wherein a combination of a laminar flow field and an electricalfield leads to ions separating, comprising the steps of:

[0014] (a) introducing a stream of charged particles or ions of variouselectrical mobilities into said analyzing region;

[0015] (b) laminarizing a flow of a particle-free sheath gas, andintroducing said sheath gas into said differential mobility analyzerimmediately upstream of said analyzing region;

[0016] (c) maintaining the flow of said sheath gas within said analyzingregion as laminar flow;

[0017] (d) providing an electrical field in said differential mobilityanalyzer, said electrical field being produced by a combination ofelectrodes and grids charged to various voltages and charging devices tomaintain said electrodes and grids at said various voltages; and

[0018] (e) sampling or collecting said separated particles or ionswithin a narrow range of electrical mobilities through at least onecollector device.

[0019] In accordance with the preferred embodiment of the apparatus, thedifferential mobility analyzer for separating ions and charged particlessuspended in a mixture comprises:

[0020] means to provide a laminar flow of ion-free sheath gas into anupstream end of an analyzing region at a Reynolds number in excess of2000;

[0021] ion supply means for introducing said ions and charged particlesinto said analyzing region;

[0022] at least two electrodes charged to suitable potentials to createan electric field within said analyzing region;

[0023] whereby said ions are separated in space by combined action ofthe electric field and the flow of sheath gas;

[0024] at least one sampling or collecting device, wherein ions of adesired mobility are sampled or collected;

[0025] power supply means to charge said at least two electrodes to saidpotentials;

[0026] means for maintaining said laminar flow within said analyzingregion; and

[0027] means to maintain flow spatial symmetry in the analyzing regionwhile minimizing pressure drop.

BRIEF DESCRIPTION OF THE DRAWINGS

[0028]FIG. 1 is a view of a low resistance differential mobilityanalyzer gas exhaust constructed in accordance with a first embodimentof the present invention;

[0029]FIG. 2 is a view of a low resistance differential mobilityanalyzer gas exhaust constructed in accordance with a second embodimentof the present invention; and

[0030]FIG. 3 is a view of a geometry for a two-dimensional fluid flowthrough the differential mobility analyzer.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS OF THE INVENTION

[0031] The instant invention comprises a method to keep the flow laminarat Reynolds numbers (Re) well above 35,000, the maximum value at which acarefully prepared DMA flow (with a large inlet trumpet) betweencylinders or parallel plates has been previously seen to remain laminar.The new method stabilizes the flow by accelerating it. This feature isdiscussed in de la Mora, de la Mora, Diffusion Broadening in ConvergingMobility Analyzers, J. Aerosol Science, Vol. 33, pp. 411-437 (2002), thesubject matter of which is herein incorporated by reference in itsentirety.

[0032] Generally, the present invention enables for the first time theattainment of high Reynolds numbers in excess of 10⁵ under laminarconditions, and, with, the improvements discussed below, further enablesthe construction of DMAs capable of ΔZ/Z (based on the full peak widthat half height, FWHH) values as small as 0.01, even for particles withdiameters smaller than 2 nanometers.

[0033] Another aspect of this invention overcomes the problem of highlosses at the inlet of cylindrical DMAs in the case of initially neutralspecies, such as drugs and explosives, by charging them immediatelyupstream of the inlet slit.

[0034] Still another aspect of this invention overcomes the priorincompatibility between short DMAs capable of high resolution in thenanometer size range, and long DMAs, capable of analyzing particles aslarge as 30 to 100 nanometers, including the means to make axisymmetricDMAs capable of high resolution analysis of particles at ΔZ/Z values of1% over the full diameter range from 2 nanometers up to 30 nanometersand beyond.

[0035] The various attributes of the present invention can be readilyunderstood with reference to FIGS. 1 and 2.

[0036]FIG. 1 describes a differential mobility analyzer of the instantinvention for separating particles or ions suspended in a gas,comprising: an analyzing region (13) in which ions are injected throughslit (4) into a flow of ion-free sheath gas. This flow is introduced in(1) and is made highly laminar by passage through several screens (2, 3)of high uniformity, and then by acceleration through a convergingsection (5). The ions are injected into the analyzing section (13) froman inlet chamber (12) whose cross section and slit width (4) aredesigned so as to provide a relatively uniform ion stream along thelength of the slit. The ions may be introduced from the outside throughport (16) into the inlet chamber (12), or may be produced there by meansof a charging device from volatile species ingested through port (16).Such a charger is incorporated in FIG. 1 in the form of a strip of ⁶³Ni(15). At least two electrodes or grids (14 and 6) spaced apart from eachother and charged to different voltages create an electric field in theanalyzing region (13), which displaces the ions injected in (4) acrossstreamlines, and directs those having certain desired electricalmobilities into one or several collecting or sampling devices, such asthe sampling slit (7).

[0037] The apparatus further comprises a flow constriction leading to anozzle (8). In the embodiment of FIG. 1 this nozzle (8) serves thepurpose of isolating the working region (13) from other regions furtherdownstream, in order to avoid or reduce perturbations on the axisymmetryof steadiness of the flow in the working region. This constriction (8)is nonetheless moderate in the present invention in order to minimizepressure drop through the apparatus, thereby enabling attainingrelatively high velocities and Reynolds numbers. To further isolate theanalyzing region (13) from the pump moving the sheath gas flow, a firstexhaust chamber (9) is provided downstream from the throat (8), which isin turn connected by means of at least three symmetrically placed tubes(10) (only two are shown in FIG. 1, of the ten actually present in theprototype rendered) to a second exhaust chamber (11). The intent of suchbuffers between the working region (13) and the exhaust line (17) goingto the pump is to avoid propagation upstream of the flow asymmetriesexisting on the downstream end of the instrument, but to do so with arelatively small pressure drop. Loss of axisymmetry in the workingregion would be fatal to resolution. Prior art has made use of only onesheath gas exhaust port. To avoid flow asymmetry potentially associatedto higher gas speeds on the side of the instrument where this port isplaced, a high pressure drop needs to be created in such designs betweenthe position of the sampling slit (7) and the sheath gas exhaust port(17). The new multiport design of FIG. 1 greatly reduces the angularvariations of gas pressure in the sheath gas exhaust chamber, allowing acomparable reduction in the required flow resistance. A secondaryexhaust chamber (11) acts as a manifold that collects the variousstreams from the primary exhaust chamber into a single final exhaustport (17). The dimensions of the second exhaust chamber (11) are alsosuch that the angular variations of pressure are small compared to thealready small pressure drop along each of the ten exhaust lines.

[0038]FIG. 2 describes a second alternate embodiment of the instantinvention, where the exhaust system is completely axisymmetric and noconstriction is introduced upstream of the diffuser (33, 38). A slowlydiverging diffuser following the sampling slit (40) enables substantialpressure recovery. This diffuser (33, 38) is essential in order toapproach sonic conditions at the throat with high efficiency householdvacuum cleaner motors, whose maximum pressure rise is generally wellbelow ½ of an atmosphere, even in tightly encased two-stage systems. Theapparatus differs principally from that described in FIG. 1 in the needto suspend the central electrode (42) from upstream, rather thandownstream of the working section. Its support is a perforated piece(43), which also supports the outer elements of the DMA, including thelaminarizing trumpet (44) and the laminarization screens (45, 46).

[0039] In the embodiment shown in FIG. 2, flow diffusion is achieved byintroducing divergence not only in the final region of the innerelectrode (33) but also at the end region of the outer electrode (38).But divergence in only one electrode would often suffice. One must notethat the conventional criterion allowing diffuser semi-angles up to 3.5degrees may not necessarily be appropriate under present conditions, asthe inlet flow differs from the standard designs in being initiallylaminar rather than turbulent, which makes the flow far more prone toseparate from the walls, reducing drastically diffuser efficiency.Thanks to the upstream support of the inner electrode, the exhaust lineis completely axisymmetric and can be integrated directly to a high flowpump such as those commercialized by AMETEK (lamb electric division) forhousehold or industrial central vacuum systems. Most desirable for thepurpose is a clean pump where the gas is compressed without being passedthrough the motor region where it would be contaminated by dust. Alsopreferred are fully encased pumps whose exhaust gas is collected into asingle outlet duct, which enables it being recirculated back into thesheath gas inlet of the DMA (perhaps through a drying and filteringsystem if necessary). Notice also in the design of FIG. 2 that thesupporting structure for the inner electrode is upstream thelaminarization screens, in a relatively wide region where speeds aresmall, even in the perforated portion (44) of the main support piece(43). The pressure drop is therefore considerably smaller than in thedesign of FIG. 1. Furthermore, the slight loss of axisymmetry induced bypassage of the flow through perforated support (44) is removed by thesubsequent passage through the laminarization screens (46 and 45).

[0040] A slightly converging electrode geometry delays boundary layertransition to Re well above 10⁶, even in the presence of free streamturbulence levels of one or a few percent. Such levels can be attainedwith a moderately small inlet trumpet, such as that employed in theVienna DMA, and do not require use of the large trumpet inlet proposedin U.S. Pat. No. 5,869,831. Although large inlet trumpets have thedesirable advantage of reducing free stream turbulence, they are by farthe bulkiest, heaviest and most expensive component of the DMA. It istherefore wise to avoid their use whenever such high degrees oflaminarization are not absolutely essential to assure proper DMAperformance. Free stream turbulence levels of 1% are certainlycompatible with the attainment of resolutions of the order of 100,better than the current world record (close to 70) reached with a DMAprovided with a large trumpet inlet but no converging working section.

[0041] One embodiment of the proposed converging DMA concept is shown inFIG. 1 for the case of an axisymmetric DMA. They combine particle-freefluid flow (the sheath gas introduced through (1)) and electric fieldsto drive charged particles introduced through a first narrow slit (theinlet or injection slit (4)) located in a first electrode or grid (14)into a second narrow slit or collector device (the outlet or samplingslit (7)) located in a second electrode or grid (6). The space betweenthese two slits and electrodes will be referred to as the “workingsection” of the DMA. A particle-free sheath gas is introduced into afluid flow inlet (1). Ideally, among the particles introduced throughthe injection slit, only those with mobilities contained within arelatively small range ΔZ centered about a mean value Z are sampledthrough the outlet slit. The inverse of the ratio ΔZ/Z is a measure ofthe DMA resolution.

[0042] Similar considerations do apply for non-axisymmetric geometries.To avoid boundary layer growth even upstream of the working section, theouter electrode or grid (5) in FIG. 1 is converging down to the inletslit (4). Hoppel, The Ions in the Troposphere: their Interactions withAerosols and the Geoelectric field, Ph.D Dissertation, CatholicUniversity of America (1968) and Hoppel, Measurement of the MobilityDistribution of Tropospheric Ions, Pure and Applied Geophysics, Vol. 81,pp. 230-245 (1970), (1968, 1970), designed and built a planarwedge-shaped aspiration counter with straight converging walls. Hoppeldescribed some key advantages associated to his convergent geometry.However, he did not reach Reynolds numbers in the high range of interesthere, and his work did not demonstrate a resolution anywhere near thevalues sought here and required for chemical and biological analysis.Furthermore, aspiration counters differ in many ways from DMAs, sincethe full flow rather than a small part of it carries charged particles.This makes it undesirable to use a large laminarization chamber withinlet filters and screens, so that convergence in the working region ismore necessary than in DMAs. Aspiration counters do not have either aninjection slit, so that the stabilization requirements in theseinstruments are considerably milder than in DMAs.

[0043] Unusually large acceleration at the injection slit or downstreamfrom it, stabilizes the associated mixing layer, even at the very largeReynolds numbers of interest here. This goal is achieved partly as inthe Vienna DMA by a slight convergence of the outer electrode (5)immediately following the inlet slit (4) (FIG. 1). But considerablyhigher convergence may sometimes be desirable. One extreme embodiment ofthe present invention's high stabilization of the mixing layer at theinlet slit is shown in FIG. 1, where the leading edge of thebullet-shaped inner electrode is located in the immediate vicinity ofthe inlet slit section. Prior art has placed this bullet top farupstream of the inlet slit. There it serves the useful purpose ofaccelerating the flow and hence reducing the relative importance offree-stream turbulence. However, it does not help stabilize the mixinglayer, which is the most fluid-dynamically unstable region of the wholeflow field. Aside from its stabilization advantage, the lowering of thebullet forces a departure from the strong tendency of prior art to usenearly parallel plate or cylindrical geometries, where the theoreticalresponse function of the DMA is easily calculated and no calibration isneeded to infer particle or ion mobility. The advantage of acalibration-free instrument is sacrificed in the present invention infavor of the preferred goal of increasing resolution. The need forcalibration is inevitable here in view of the fact that the wholegeometry needs to be convergent. However, precise mobility standards forcalibration have recently become available in the nanometer range, sothat the traditional reasons for favoring non-converging geometries nolonger apply.

[0044] De la Mora (2002) demonstrated theoretically that the quantity Hrelated to DMA resolution is unity under the best of circumstancesconsidered, and larger than unity in all other cases studied, and referswithout detail to different unpublished geometries discovered by Dr.Michael Labowsky (Wayne, N.J.), for which H can be smaller than unity,and which are therefore superior to those previously known. One exampleof such special geometries is provided in FIG. 3 for two-dimensionalflows, where the central element is at ground and the two elementssurrounding it are raised to the same voltage. Inlet and outlet slitsare indicated (I and O) as well as an ion trajectory (T) going throughboth slits. Labowsky's design differs from the geometries considered inde la Mora (2002) in that the boundary conditions for the streamfunction and the voltage do no longer coincide with each other at theplane of symmetry. The same feature arises in axisymmetric flows ingeometries where the inner electrode is bullet-shaped, such in the DMAof Rosell et al. However, for this feature to yield H values below unitycertain special precautions are necessary. One possible approach is tolower the bullet nose from its traditional position (well above theinlet slit) into a region closer to the inlet slit, or downstream fromit, where its electric field is felt by the ions as they emerge throughthe inlet slit. The axisymmetric analog of FIG. 3 provides anotherexample where the same advantage arises. Again, the advantage requirescertain unusual features, such as the proximity characteristicmentioned, which are not met any axisymmetric or two-dimensional DMAbuilt to date.

[0045] We note that the extreme acceleration shown in FIG. 1 in thevicinity of the inlet slit (4) may not be necessary in many cases wherea more slowly converging geometry would assure the stability of themixing layer following the aerosol inlet. In such cases it is in factpreferable to moderate the abruptness of the convergence for severalreasons. First, the flow field will be more uniform, which in turnfavors overall stability. Second, de la Mora (2002) has shown thatexcessive acceleration often leads to a loss of resolution with respectto the value given in equation (1) for the case of a cylindrical design.Third, earlier acceleration would reduce earlier on the level of freestream turbulence, which would hence be smaller if the leading edge ofthe electrode (6) were to be placed further upstream than shown in theembodiment of FIG. 1.

[0046] An alternative embodiment of the present invention acceleratesthe flow by a combination of various degrees of convergence on the outerand inner electrodes. In addition to the stabilization advantages justdescribed, we note the fact that U.S. Pat. Nos. 5,869,831 and 5,936,242protect DMAs with a laminarization system delivering a laminar flow atReynolds numbers above 2000 into the working section inlet. Byintroducing acceleration in the working section, the present inventioncovers situations where the laminarizing means provides laminar flowsbelow 2000 to the inlet of the working section, but subsequentacceleration within the working section may increase considerably theReynolds number in downstream regions of the working section. Asdiscussed in de la Mora (2002), considerable acceleration (henceincrease in Re) can be achieved in axisymmetric geometries withacceptable resolution loss. Since the resulting resolution is primarilydetermined in the final portion of the working section (where Re ishighest in such accelerating designs), it is possible without making useof the above mentioned U.S. patents to attain resolving powers muchlarger than in nonconverging DMAs running at Re<2000.

[0047] A design including low-resistance sheath gas exhaust greatlyreducing the pressure drop through the instrument, enables attainment ofgas velocities well in excess of 100 m/s with relatively light andinexpensive pumps, such as those used in high efficiency householdvacuum cleaners and central vacuum cleaners.

[0048] Another embodiment of the present invention comprises a method toachieve better laminarization conditions at the beginning of the workingsection than previously obtained, even with a large inlet trumpet. Thisnew method uses a small inlet trumpet, such as that in the Vienna or theRosell DMAs. At sufficiently large sheath gas flow rates, the flowpassing the inlet screen becomes turbulent. This turbulence survives fora certain distance downstream, which appears as undesirable from theviewpoint of achieving a highly laminar flow On the other hand, thisturbulence provides excellent mixing, and the flow becomes highlyuniform on the average. Hence, provided that this flow returns to alaminar state before it reaches the inlet slit, the introduction ofturbulence in the screen is desirable rather than undesirable as ityields a highly uniform as well as a highly laminar flow. The presentimprovement therefore involves (a) choosing a screen cross-section,transparency, and wire diameter such that (at a given gas flow rate) theflow through the screen becomes turbulent. The criterion for this tohappen is well known to fluid dynamicists, and involves a Reynoldsnumber about the screen wire larger than about 40, (based on local speedand wire diameter), when the Karman vortex street sets in; (b) Using amoderately converging geometry following the screens, such that, if theflow were laminar, it would remain laminar, while a turbulent flow wouldtend to relaminarize; and (c) Choosing a sufficiently long distancebetween the screen and the aerosol inlet slit, and making the screenwires and opening sufficiently thin for the turbulent flow to actuallyrelaminarize before it reaches the aerosol inlet slit. Note thatrelaminarization at high flow Re in the channel requires a convergentwall, such as discussed in de la Mora (2002). But, as discussed, it doesnot require a high convergence angle, so that a relatively modestconvergence ratio (such as that in the Reischl or the Rosell DMA)provides a relatively long path for relaminarization. Hence, it ispreferable to use small convergence angles (yet large enough to assureflow stability as discussed in de la Mora (2002)) because this providesa greater downstream distance for relaminarization. The requiredrelaminarization distance is well known to fluid dynamicists familiarwith the field of grid turbulence. It can be accommodated in moderatelysized designs by making the screen wire and opening sufficiently small,and making the distance between the screen and the inlet slitsufficiently long For example, a screen transparency of 27% with screenwire diameter of one or a few thousands of an inch followed by a conicalsection with a half angle of 10 degrees enables substantialrelaminarization considerably before the flow cross section is reducedto ⅕ of its initial value. For this scheme to function successfully, itis not essential that the flow becomes turbulent past the screen,provided that the screen is highly uniform, as many commerciallyavailable screens actually are. Hence, earlier art based on large inletscreens where the flow does not become turbulent is also suitable toproduce a uniform laminar flow. However, there is an advantage inattaining this laminar state with a small trumpet, as the manufacturingcost and weight of the instrument can be drastically reduced.

[0049] A disadvantage of the small over the large inlet trumpet is thata small screen area with a small screen transparency tends to producehigh pressure drop, and hence yields a smaller flow rate with a givenpump. The present invention includes a means to counteract this problemwithout making use of previous art based on large laminarizationtrumpets. The new procedure uses first a wide flow cross-section withone or several filters, and one first screen of low transparency (say30%). The flow resistance is small in spite of the low transparencybecause the area is large. Then follows a convergent region, and finallythe true laminarization screen with small cross section, as described inpoint 3. The difference with 3 is that this laminarization screen mayhave a large transparency and hence a low pressure drop, without loss ofthe advantages described in point 3. In other words, prior art usedfirst a low transparency screen and a high transparency screen forlaminarization, both in a large cross sectional area, followed by aconvergent region. This arrangement is typical of wind tunnel inletdesigns, and is widely used in fluid mechanical laboratories. Thepresent invention uses a high cross-sectional area only for the upstreamfilters (if any) and the low transparency screen, and introduces thehigh transparency screen somewhere within the convergence region. Itincludes all the advantages described above without the disadvantage ofthe high pressure drop.

[0050] Another preferred embodiment of the present invention is suchthat the maximum displacement of the axis of one cylinder from the axisof the other is less than one thousandth of an inch, preferably lessthan half a thousandth of an inch.

[0051] Knutson, The Distribution of Electric Charge Among the Particlesof an Artificially Charged Aerosol, Ph.D. Thesis, University ofMinnesota (1971) considers the effect that a parallel displacement 0 ofthe axis of one of the cylindrical electrodes with respect to the axisof the other cylinder has on DMA resolution. His numerical results forthe particular case of the DMA disclosed in Knutson et al., AerosolClassification by Electrical Mobility: Apparatus, Theory andApplications, J. Aerosol Sci., Vol. 6, pp. 443-451 (1975) show that thefull width of the resulting distribution broadening ΔZ/Z would be closeto 4ε/(R₂−R₁):

ΔZ/Z=4ε/(R ₂ −R ₁)+O(ε²).   (5)

[0052] Our analysis in the limit of small eccentricity ε shows that thisresult is almost independent on the ratio of radii when R₁/R₂>0.5.

[0053] Both results hold only in the absence of other broadeningmechanisms such as diffusion. We also find that the instrument'sresponse function f(Z) has turning points at its edges Z=Z_(o)±ΔZ/2.This makes it singular, so that the more commonly used measure of ΔZbased on the full distribution width at half height (FWHH) is also equalto 4ε/( R₂−R₁). The goal of attaining FWHH values as small as 1% hencerequires ε<0.01 Δ/4. For Δ=0.5 cm, ε must be smaller than 12.5 μm (0.49thousands of an inch). Such tolerances are considerably more demandingthan those previously attained in commercial DMAs, but are mostdesirable for the objectives of the present invention.

[0054] Consider now a situation where the eccentricity is 0.0005 inch.When the DMA is mounted on a lathe centered with respect to one of theelectrodes and an indicator is placed on the other electrode, themaximum displacement of the indicator will then be 0.001 inch. Thisvalue is typical of a good machining job, since at least half thatclearance between critical parts is necessary for them to fit into andout of each other, unless special surface treatments such as grinding orhoning are applied (however, much better centering can be obtained withconical rather than cylindrical fittings). The DMA of FIG. 1 has threesuch critical fittings. If ΔZ/Z<1%, then εR₂/(R₂−R₁) must be smallerthan 0.25%. When εR₂<0.0005″, this requirement can be reached providedthat R₂−R₁>5 mm, but is more easily met in a DMA with twice that gap.Such tolerances are considerably more demanding than those previouslyattained in commercial DMAs, but are most desirable for the objectivesof the present invention. These results hold only in the absence ofother broadening mechanisms such as diffusion.

[0055] The previous calculation is based on the assumption that thevelocity field is either flat or fully developed. However, the presenceof eccentricity would tend to create an angular dependence of the widthof the throat region. According to Bernouilli's law, the gas speed atthe throat would be angularly uniform. But if the gap is not uniform,the local flow rate per unit length Q would also vary along the slitlength. The flow speed in the working section would then be smaller inthe regions with a narrower gap, where the radial field is larger andthe radial distance to travel is smaller. This additional effect islikely to turn FWHH into 6ε/(R₂−R₁) instead of the more conservative4ε/(R₂−R₁) given in equation (5). Although such conclusions are drawnfor the case of a plane or cylindrical geometry, they apply with slightcorrections to the case of slowly converging geometries such as that ofFIG. 1. They hold also approximately in more rapidly converginggeometries.

[0056] The DMA of Knutson et al. (1975) provides for an axisymmetricinjection of the aerosol flow through the inlet slit. This design,however, is associated to large losses of particles smaller than 5nanometers by diffusion to the aerosol inlet walls. This problem ispartly overcome by the split-flow design in the nanoDMA of Chen et al.,Design and Numerical Modeling, presented at the AAAR Annual Meeting,Orlando, Fla., Oct. 14-18 (1996), and Chen et al., Numerical Modeling ofthe Performance of DMAs for Nanometer Aerosol Measurement, J. AerosolSci., Vol. 28, pp. 985-1004 (1997). However, this design has not yetdemonstrated an ability to transmit and size particles with diameterssmaller than 3 nanometers. In contrast, the Vienna DMA introduces theaerosol stream through a short lateral tube into an aerosol inletchamber immediately preceding the inlet slit. Losses of very smallparticles are thereby greatly reduced with respect to truly axisymmetricdesigns, with a demonstrated ability to transmit even small ions. Thisimprovement, however, comes at a cost. As represented in FIG. 1, theinlet chamber (12) is annular or straight for cylindrical ortwo-dimensional DMAs, respectively, both cut on one side by the slit(4). The flow of aerosol through the slit into the working chamber isdriven by the difference in pressure of the gas upstream and downstreamthe slit. But since the aerosol stream has to travel from the inlet tubealong this inlet chamber to reach all points of the slit, and thistravel requires a certain pressure drop, the aerosol tends to reach theworking region of the Vienna DMA predominantly through the portion ofthe slit facing directly the aerosol entry tube. Swirl may perhapsreduce this problem, but does not eliminate it. Two main problems followfrom this asymmetry. First, since the peak width ΔZ increases linearlywith the local ratio of the aerosol to sheath gas flow rates, it islarger than the average at some points, which reduces the resolution ofthe instrument. Second, the shear layer instability that tends to arisefollowing the injection slit can be moderated by suitable choice of theratio of mean speeds between the aerosol and the sheath gas. Thiscontrol, however, becomes harder when the aerosol flow is not uniformalong the slit length.

[0057] The aerosol injection chamber is designed in the presentinvention such that the pressure drop along the perimeter of the chamberis much smaller than the pressure drop across the slit. This goal isachieved by making the cross section of the chamber sufficiently largeand the injection slit channel sufficiently narrow and long.

[0058] The correct selection of the width δ_(i) of the aerosol inletslit is of considerable importance, and an improper choice can lead topoor resolution for a variety of reasons. At first glance it wouldappear that δ_(i) must be relatively narrow at the scale of the axialdistance L between the two slits, or else the initial spatial spread ofthe aerosol flow would reduce resolution. However, the electric fieldaccelerates radially the entering aerosol and immediately makes itsaxial cross section relatively independent of δ_(i). Consequently, thisfirst criterion leaves δ_(i) free. A second criterion putting bounds onδ_(i); is that it should not be so small as to form a wall jet movingfaster than the sheath gas, since this would tend to destabilize furtherthe mixing layer. Under operating conditions leading to high resolution(q_(a)/Q<0.01), and using a ratio δ_(i)/L larger than 0.01, thisrequirement is almost always met. Hence, although the aerosol speed willgenerally be smaller than the sheath gas speed, the intense accelerationimposed in this region still assures stability. Under certainconditions, such as for instance, when analyzing particles past theupper size range of the instrument, it may be necessary to reduce Qbelow 100 or even 30 liters/minute, which is likely to force use ofq_(a)/Q ratios well above 1%. For such cases, it is essential toincrease δ_(i) so that the aerosol ejection speed does not exceed toodrastically the mean sheath gas speed. The slit width of the DMA shownin FIG. 1 can be changed by inserting shimstock pieces at the union ofthe two pieces defining the slit. Another consideration suggesting theuse of larger rather than smaller inlet slit widths is the fact thatdiffusion losses increase as 1/δ_(i). The variable slit design of thisinstrument therefore allows its widening in cases when the signal is toosmall, and a reduction of transmission losses carries more weight thanother considerations.

[0059] Accordingly, the ideal range in this invention for the verticalelevation of the inlet slit top over its bottom is between 0.025Δ and0.1Δ, with a preferred value of 0.05Δ. The dimensions of the aerosolchamber preceding the inlet slit in the cylindrical DMA of FIG. 1 havebeen determined such as to meet the requirements of the previousparagraph using the preferred elevation of 0.05Δ. An excessive chambercross section is undesirable because it would promote the loss of smallcharged particles by space charge.

[0060] A serious difficulty associated to axisymmetric DMAs is therelatively high loss of nanometer particles through its inlet up to thepoint past the aerosol injection slit. Such losses are particularly highin the case of intense sources of unipolarly charged particles, such aselectrosprays. A solution to this problem was proposed in U.S. Pat. No.5,869,831 involving a planar DMA configuration with two orifices ratherthan two slits. That principle can be used similarly in the case of DMAswith converging walls, and is thereby incorporated into the presentinvention, either for mass spectrometric applications or for otherpurposes.

[0061] Axisymmetric DMAs may therefore not be the most competitiveinstrument in dealing with certain analytical applications with intenseunipolar ion sources at atmospheric pressure. However, in situationssuch as monitoring of explosives or drugs, where the volatile species tobe detected are initially neutral, there would be no loss of analyte atthe inlet of the DMA. In other cases where a neutral analyte is volatileat temperatures higher than that at the DMA inlet line, losses bydiffusion may stilt exist, but the generally stronger losses associatedto space charge would still be absent.

[0062] In such situations and in many others, an axisymmetric DMAgeometry such as that shown in FIG. 1 offers advantages over the twoorifices placed in two parallel or converging walls just discussed inrelation to U.S. Pat. No. 5,869,831. The reason is that, at sheath airflow rates of 3000 liters/minute, the aerosol flow could, without lossof resolution, be as high as 30-60 liters/minute. This flow rate is vastcompared to the throughput that can be passed through a typicalatmospheric pressure inlet to a mass spectrometer, and would be ideallysuited for situations involving highly dilute and difficult to detectanalytes. In such cases, the species to be detected would be charged inthe aerosol inlet chamber, immediately upstream of the injection slit,thereby minimizing the loss of analyte ions by diffusion to the wallsonce they are formed. A variety of schemes can be used for the purposeof charging the analyte vapor molecules, including a radioactive sourceplaced through the whole or a portion of the perimeter of the aerosolinlet chamber (for instance, a ring or a washer of ⁶³Ni, ²¹⁰Po, oranother alpha or beta emitter). In this case, some of the considerationsmade earlier regarding the dimensions of the aerosol inlet chamber wouldhave to be modified in order to assure a suitable charging efficiency,though those familiar with the problem of charging of small ions andultra fine particles in such environments can readily design such achamber. Note that an inlet chamber larger than that of FIG. 1 willoften be required, but will not increase unreasonably the losses of ionsunder the present in-situ charging conditions. Therefore, this inventionalso includes variously converging axisymmetric DMAs with a radioactivesource spread over all or part of its aerosol inlet chamber. We notethat charging schemes other than those relying on radioactive sourcesare also included within the scope of this invention. In fact, IonMobility Spectrometry; by Eiceman et al. (CRC Press, FL, 1994) discussesthe complexity of the ion types produced by radioactive sources, and theneed for using highly purified gases that may not be easily provided atthe rates required for the sheath flow in a DMA. Cleaner ion sourcessuch as, for instance, those developed by F. Eisele and colleagues Refwould therefore be even more useful for the analysis of volatiles inDMAs.

[0063] Another objective of this invention is to identify conditionsenabling the construction of DMAs enjoying both wide size range and highresolution operation.

[0064] The short DMA of Rosell et al. (1996) has a length Lapproximately twice the optimal value L*, and achieves as a result aresolution in the nanometer range substantially higher than the similarbut much longer Vienna DMA, where L/L* is close to 15. However, thegains in resolution obtained for very small particles in the short DMAcome at the cost of loss of the ability to analyze larger particlescharacteristic of the long DMA. This is a direct result of the factthat, all other things being equal, the mobility of the particlesselected by the DMA varies inversely with its length L:

Z ⁻¹=2πLV 1n(R ₂ /R ₁)/Q,   (6)

[0065] where V is the voltage difference applied between the twoelectrodes.

[0066] A general problem with all the DMAs discussed so far in theliterature, including those commercially available from TSI and Hauke(Vienna model) as well as short experimental models is that, if theywork well with very small particles, they tend to have a limited rangewith larger particles, or if they can cover the range of largeparticles, they tend to have a poor resolution with very smallparticles. Since manufacturers of long or medium size DMA often make theclaim that their instruments are suitable for the analysis of particlesas small as one or a few nanometers, while those of medium size DMAssometimes do also claim an ability to analyze particles as large as 100nanometers, we will subsequently define the proper range of aninstrument in terms of the maximum and minimum mobilities Z_(max) andZ_(min) which they can analyze with a resolution higher than a certainminimum. Without that minimum resolution constraint, it is clear thatthere is no upper or lower limit for Z, since either the voltage V orthe flow rate can in principle be reduced to arbitrarily small values.Considering the substantial number of DMAs built to date, it would seemthat the hope of designing one DMA able to deal simultaneously withsmall as well as large particles is futile. The notion that analyzingparticles 50 or 100 nanometers in diameter calls for relatively longDMAs, while particles a few nanometers in diameter require short DMAsare both well established in this field. These impressions are in factreadily proven to be inescapable in the case of two-dimensional ornarrow gap cylindrical DMAs (R₂/R₁−1=Δ/R₁<<1), when (6a) reads$\begin{matrix}{{Z = {\frac{Q}{2\pi \quad R_{1}}\quad \frac{\Delta}{L\quad V}}};{{{{when}\quad {R_{2}/R_{1}}} - 1} = {{\Delta/R_{1}}\quad {1.}}}} & \left( \text{6b} \right)\end{matrix}$

[0067] The group Q/(2πR₁) is just Q′, the flow rate per unit lengthcharacteristic of the two-dimensional geometry, so that ZV/Q′=Δ/L. Sincethe quantities V and Q are limited to a certain finite range, it isclear that long DMAs with larger values of L/Δ favor small particles,and short DMAs have the opposite property.

[0068] Such a situation is unproblematic for a number of applications.For instance, the identification of drugs and explosives by mobilityanalysis requires instruments capable of dealing only with particlessmaller than 3 nanometers, for which a short DMA suffices. Mosttraditional DMA applications deal with particles larger than 5nanometers, for which the long Vienna design is more than adequate.However, there are other applications where high resolution in the 2-5nanometers range is as essential as the ability to analyze particles aslarge as 30 nanometers. One example is in monitoring industrialpolymers, where the molecular weights of interest span the range fromseveral thousand amu (2-3 nanometers) to several million amu (15-30nanometers). In this case, the powerful and widely used technique ofelectrospray mass spectrometry fails to offer a satisfactory analyticalsolution due to peak congestion associated to the presence of manymasses, each in numerous different charge states.

[0069] (MALDI) Matrix assisted laser desorption ionization massspectrometry is in principle less prone to peak congestion since ittends to produce mainly singly charged ions. But the ionization processis strongly dependent on polymer mass as well as the chemical nature ofthe analyte and the matrix, which makes problematic the quantitation ofpolymer mass distributions over their typically broad mass ranges. Themasses in the related problem of protein or nucleic acid analysis rangesimilarly from several thousand amu, up to several millions. Thissituation is often, but not always, amenable to electrospray massspectrometric investigation, and would also benefit from theavailability of alternative fast and inexpensive techniques such as thatprovided by DMAs. Since DMAs have a much higher mass range than massspectrometers, the procedure of reducing to unity the charge ofelectrospray ions is still compatible with their mobility classificationat mass to charge values even beyond 10⁷ amu. In these important twoexamples just mentioned, and probably in many others, it would be veryuseful to develop a DMA capable of covering at high resolution the wholesize range, from at least 2 nanometers up to 30 nanometers.

[0070] Equation (6) shows that, for a given cylindrical DMA geometry(given R₁, R₂ and L), the smallest value of Z attainable (lowestmobility range) corresponds to the largest voltage and the smallest flowrate. Brownian motion is generally relatively weak in the small mobilityregion, so that the main factor limiting resolution (in mechanically andfluid dynamically well designed instruments) is the ratio q_(a)/Q ofaerosol to sheath air flows. Resolution is highest when the aerosolinlet flow is close to the aerosol outlet flow, and we will consideronly this most favorable situation, where FWHH is equal to q_(a)/Q. Theresolution criterion that FWHH be smaller than 1% therefore fixes thisflow rate ratio to be smaller than 1%. Clearly, less stringentresolution standards would allow smaller flow rate ratios. In principle,the constraint q_(a)/Q<0.01 places no direct limits on Q. In practice,however, most existing detectors for nanoparticles and ions use aerosolflow rates q_(a) of the order of 1 liter/minute. Losses in thetransmission lines tend to be substantial at lower flow rates, andserious detection difficulties tend to appear. We will therefore basethe following estimate on a minimum acceptable aerosol flow rate of 1liter/minute, and a corresponding Q_(min)=100 liters/minute. Muchsmaller Q values are commonly used in DMAs, but they are invariablyassociated to resolutions much smaller than set here. The nextconsideration is how large V can be. The limit is imposed by theappearance of electrical discharges. This limit is generally weaklydependent on the ratio R₂/R₁, and essentially independent on L.Therefore, a value of 10⁴ volt, typical of commercial DMAs, will beadopted. With the choices V_(max)=10⁴ volt and Q_(min)=100 liters/minutewe find Z_(min)=C/(L 1n(R₂R₁)), which in terms of the variables L* and bof equations (2-3) may be written:

Z _(min) =C/(bL* 1n(R ₂ /R ₁)); C=0.2652 cm³/s.   (7a,b)

[0071] In order to offset the strong peak broadening effects in thehighest mobility range, DMAs must operate at large sheath air flowrates. Hence, the ratio q_(a)/Q is typically smaller than 1%, and theresolution of a well designed DMA is well described by equation (1). Thecondition ΔZ/Z<1% then implies that D/(L*U) (b+1/b)<1.85×10⁻⁵.Expressing D in terms of Z via (4) and using Q=π(R₂ ²−R₁ ²)U, we find

Z _(max) =A L*/(R ₂ ² −R ₁ ²)/(b+1/b);   (8a)

A=1.85×10⁻⁵ eQ/(2πkT).   (8b)

[0072] In the case of particles or ions carrying z elementary charges,the constant A would be further multiplied by the charge state z. Wewill nonetheless base the discussion on the least favorable conditionwhere z=1, since this situation simplifies the interpretation of amobility spectrum as a size distribution. Evidently, the larger Q thehigher the mobility that falls within the analyzable range. Highefficiency household vacuum cleaners or central vacuum systems reachflow rates larger than 3000 liters/minute provided that the pressuredrop is moderately small, as is the case of DMAs built according to thepresent invention. We will therefore base the present estimate on avalue of Q_(max) of 3500 liters/minute. Considerably larger values canbe obtained by combining two or more such pumps in parallel. At roomtemperature, this yields

A=6.7 cm ³ /s.   (9)

[0073] A most important quantity characterizing the instrument's rangeis the ratio Z_(max)/Z_(min):

Z _(max) /Z _(min)=(A/C)F(R ₁ /R ₂)/(1+1/b ²);   (10)

F(y)=1n(1/y) (1−y ²)/(2+2y ²)   (11)

[0074] The group A/C takes the value 252 in the present estimate, butcan be made considerably larger by relaxing the resolution requirement.The group (1+b⁻²)⁻¹ plays a limited role, because only the domain b>1 isof practical interest. In this region, (1+b⁻²)⁻¹ varies only from ½(b=1) to 1 (b=∞). Even at b=2, at which the resolution is very close tothe optimal value corresponding to b=1, the factor (1+b⁻²)⁻¹ differsonly by 20% from unity. At b=3, (1+b⁻²)⁻¹=0.9. Once b>3, (1+b⁻²)⁻¹approaches closely its large b asymptote where both Z_(max) and Z_(min)decrease linearly with L (or b), so that their ratio is independent ofb. In contrast, the ratio R₁/R₂ has a very strong effect on the rangethrough the function F, as illustrated in Table 1. TABLE 1 Function Fdefined in Equation 11 F(y) 0.5 0.487 0.452 0.4328 0.413 0.395 0.3470.28 .252 .213 y 1 0.757 0.56 0.5 0.444 0.4 0.3 0.2 0.15 0.1

[0075] The range function F(y) increases monotonically with y, andreaches its largest value F_(max)=½ in the vicinity of y=1 (2-D DMAlimit). Although there is a considerable penalty against DMAs with widegaps (where R₂/R₁−1 is not small), a ratio R₁/R₂=0.56 is stilltolerable, with less than 10% loss of range with respect to thetwo-dimensional limit. Under the most favorable conditions whenR₁/R₂>0.56 and b>3, the maximum ratio Z_(max)/Z_(min) is A/(2C),affording only a range of mobilities slightly larger than two orders ofmagnitude:

Z _(max) /Z _(min) <A/(2C)=126   (10b)

[0076] The range of mobilities spanned by air-suspended particles withdiameters going from 2 nanometers to 100 nanometers is considerablywider than 100, implying that it is not possible to cover it fully witha single instrument for the conditions of resolution, flow rates,voltages and temperature set here. The ratio A/C may be written as:.$\begin{matrix}{{A\text{/}C} = {\frac{\left( {\Delta \quad Z\text{/}Z} \right)^{2}}{81{n2}}\quad \frac{Q_{\max}}{Q_{\min}}\quad \frac{e\quad V_{\max}}{k\quad T}}} & \left( \text{10c)} \right.\end{matrix}$

[0077] and is therefore not necessarily fixed as 252. For instance,sacrificing a factor of two in resolution (ΔZ/Z=2%) increases Z_(max) bya factor 2² (by allowing operation at smaller voltages) and decreasesZ_(min) by another factor of 2 (by allowing operation at smallerQ_(min)). The range therefore increases strongly with slight reductionsin resolution. Q_(max) can also be increased in principle well above the3500 liters/minute set earlier. Given a large enough blower, it is infact possible to build a DMA with rather small Z_(min), while keeping bclose to the optimal value. A narrow-gap design with the same Z_(min) asthe Vienna DMA (6.45×10⁻⁴ cm²/V/s according to equation (7)) wouldrequire bR₂=41 cm, leading to an unusually wide instrument (R₂=13.66 cmfor b=3).

[0078] A more practical approach to cover the full range of particlesizes from 2 nanometers up to 100 nanometers is to use two widelydifferent lengths L by means of two interchangeable inner electrodeswith sampling slits located at different positions. Therefore, oneembodiment of the present invention capable of reaching high resolutionover an unusually wide range of mobilities consists of a DMA where oneof the electrodes is interchangeable, so that the variable b can take inone electrode configurations values in the vicinity of the optimal(1<b<4), and considerably larger values of the order of 10 in anotherelectrode configuration. This method has been used by Rosell et al.,(1993, 1996) in a DMA with the inner and outer diameters identical tothose in the Vienna DMA. Their short bullet had L=1.6 cm (b=2.143), forwhich equations (8a) and (9) yield Z_(max)=0.46 cm²/V/s (mobilitydiameter of 2 nanometers). Their long bullet had L=11.4 cm, for whichequations (7a-b) yield Z_(min)=6.5×10⁻⁴ cm²/V/s. The total range withthis combination is Z_(max)/Z_(min)=708. The sheath air outlet of theDMA of Rosell et al. (1996) was also that of the Vienna design, hadtherefore a high pressure drop, and could evidently not reach flow ratesas high as 3,500 liters/minute. This limitation is resolved in the lowresistance outlet system of FIG. 1. In this case, the throat is muchwider than in FIG. 2, the corresponding pressure drop is relativelysmall (U_(max)=40 m/s) and no diffuser is necessary.

[0079] Another embodiment of the present invention is an axisymmetricDMA of fixed geometry approaching conditions for maximum range, with apreferred geometry such that b is near 3 and R₁/R₂>0.56. A two-bulletDMA can also be implemented to widen the Z_(min) range of an instrumentsuch as that in FIG. 2, meant to cover the nanometer and subnanometerrange. However, in this case, Z_(max) is too large and R₂/R₁ too small,which precludes reaching values of Z_(min) as small as in the Vienna DMAexcept with unduly large b values (b=71 for a DMA with R₁=4 mm, R₂=9mm). This design is therefore ideal for applications such as drug andexplosive analysis requiring high resolution at high mobilities, but notso for applications requiring the widest possible range. Other specialapplications such as protein and polymer analysis can be handled with asingle-bullet design by shifting the DMA radii to values larger than inFIG. 2, while approaching the high asymptote of the range function F(y)by using a ratio R₁/R₂>0.56. For instance, taking R₂−R₁=1 cm (in orderto meet the ΔZ/Z<1% criterion with mechanical tolerances of only 0.001″)and R₂=2.3 cm (R₁/R₂=0.565), the choice b=3 (L=2.89 cm) yieldsZ_(max)=0.537 cm²/V/s (1.7 nanometers); Z_(min)=0.00523 cm²/V/s. Thiscovers the mass range from a few kilodalton to beyond 1 megadalton.

[0080] The previous considerations have been restricted to the case ofcylindrical DMAs. However, they apply approximately also to axisymmetricDMAs with slowly converging walls. They also hold qualitatively in thecase of rapidly converging walls.

[0081] An alternative means to reduce free stream turbulence proposed inthis invention is to introduce a substantial (rather than a slight)contraction within the working section. This approach differs fromearlier art, where the working section was unaccelerated and the largecontraction was placed upstream from it. This key difference leads fordiverse reasons to variations in performance between the two approaches.

[0082] We have discussed the advantages of a small sustainedacceleration within the full working section for the purpose of avoidingturbulent transition. We have pointed out that the large inlet trumpetof U.S. Pat. No. 5,869,831 placed upstream of the working section isvery useful to delay transition in the case of plane or cylindricalelectrodes. But such a large trumpet is not necessary for this purposein DMAs with converging electrodes, because the slight contraction ofthe working section provides boundary layer stabilization even with amoderate level of free-stream turbulence. There is nonetheless anadvantage of a large accelerating trumpet upstream of the workingsection, because the associated free-stream turbulence reductiondecreases peak broadening associated to velocity fluctuations. The costand inconvenience of a relatively large inlet section may in somespecial applications be desirable, such as, for instance, to achieveΔZ/Z values even smaller than 1% in mechanically very perfect DMAs runat particularly large Reynolds numbers.

[0083] Larger angles of convergence allow shortening certain parts ofthe DMA, hence reducing their weight and cost, increasing mechanicalperfection, decreasing ion losses by diffusion in the outlet line, etc.For instance, the throat preceding the sheath air exhaust must be placedat a certain distance downstream of the sampling slit. For cylindricalor plane electrodes, their surface must then incorporate relatively longconcave and convex sections, or sudden changes of slope which arefluid-dynamically undesirable. For the modest angle of convergence shownin FIG. 1, the axial distance between the throat and the sampling slitis several times the optimal DMA length L*. It could evidently besubstantially shorter with more rapidly converging electrodes. Similarconsiderations apply to the region upstream the inlet slit. In U.S. Pat.No. 5,869,831, the inlet trumpet is first concave and then convex,finishing in a direction parallel to the walls of the working section.The inlet trumpet is consequently rather long and heavy. Its length wasdecreased in the design of Herrmann by elimination of the initialconcave part and by use of a conical inlet of relatively large angle(FIG. 2). However, the transition between this converging inlet and thenon-converging working section must be gradual (therefore long) in orderto avoid flow separation. The relatively long associated transitionregions lead also to wide boundary layers at the aerosol inlet section,which precipitate transition. Most of these problems are eliminated byusing a rapidly converging working section. If the inlet trumpet (smallor large) has the same or a smaller angle of convergence than theworking section, the transition between both can be relatively short orentirely absent. At the exhaust section the distance between the nozzleand the sampling slit can be made relatively short, since neither astraightening of the jet at the inlet of the exhaust chamber is needed,nor a change of curvature or slope immediately after the sampling slit.

[0084] From the point of view of reducing free-stream turbulence andhence controlling the associated peak broadening it may seem that anapparent disadvantage of accelerating through the working section(rather than prior to it) is that the beginning of the ion separationprocess occurs at a higher level of free-stream turbulence, while onlythe final stages of the analysis proceed in a more laminar environment.The advantage of U.S. Pat. No. 5,869,831 where the full analyzing regionoccurs at a small free stream turbulence level, is undeniable. However,this disadvantage of the present invention is partially offset by theadvantages just discussed. Furthermore, the final stages of the ionmotion through the working section have a much larger impact on peakbroadening than the initial ones, so that this negative influence tendsto be substantially smaller than would seem at first sight. This can beseen by treating beam broadening associated to free stream turbulence asif it were governed by the same rules as Brownian diffusion, though withan increased effective diffusion coefficient. The role of accelerationon Brownian broadening can be illustrated by the particular case of atwo-dimensional DMA of planar walls converging at an angle α. In thiscase, the analog of the quantity b introduced in (1-2) is the groupk=ZV/Q′, where Q′ is still the flow rate per unit slit length, and,ΔZ/Z˜(k+1/k)^(1/2) (b˜L/Δ, where L and Δ are still the axial distancebetween inlet and outlet slits, and the distance between electrodes atthe outlet section). 1/k=b_(ef) plays here the role of an effective bgoverning the increase of diffusive broadening above the minimumassociated to the optimal geometry (k=1). For a two-dimensional DMA ofplanar walls converging at an angle α we may write:

bk=[ ^(eα/k)−1]/(α/k).

[0085] When α/k is small, this group tends to unity, so that the actualand diffusion DMA lengths coincide approximately. For values of k oforder one (near optimal geometry) this corresponds to small angles ofconvergence. At large angles of convergence, however, b may beconsiderably larger than 1/k. For instance, at k=⅓ and a=45°, b=12.16.In other words, although a DMA with b=12 is relatively long and onewould expect a high diffusive broadening, in reality a high convergencemakes this broadening much smaller than for a cylinder, with b_(ef) ofonly 3. In essence this means that most of the broadening action occursover the region closest to the sampling slit (where the flow is morecompletely laminarized) rather than through the more perturbed inletregion.

[0086] If a typical cylindrical DMA built according to U.S. Pat. No.5,869,831 would have a trumpet inlet radius R_(O)=52 mm and cylindricalworking sections with radii R₂=9 mm, R₁=4 mm, a typical DMA builtaccording to the present invention would have the same inlet radius, andhence the same overall width. However, at the inlet slit it would haveR₂=52/{square root}6=21.23 mm, R₁=0, with a modest contraction ratiovery close to the total area contraction ratio of 6 used previously inthe Vienna DMA between the last laminarization screen and the beginningof the working section (the inlet slit). Shortly downstream the inletslit, the inner radius would rise rapidly to its final radius of 4 mm,while the outer radius would continue converging through the workingsection at the same rate as ahead of the inlet slit, or at an evenlarger rate. The effective level of laminarization would then becomparable in both configurations, as would the diameter andeffectiveness of the laminarization screens, as well as the sheath gasexhaust section and associated pumping requirements. The new DMA would,however, be considerably shorter than that based on U.S. Pat. No.5,869,831. This would allow lengthening in the present invention theinlet region prior to the aerosol injection slit, thereby furtherdissipating the already small level of turbulence generated at the inletscreens or surviving through them. The level of convergence downstreamthe inlet slit would then be higher than upstream, with a particularlyintense flow acceleration level therefore helping stabilizing the mixinglayer.

[0087] We have discussed the advantages of creating a throat downstreamthe aerosol sampling slit in order to decouple the laminar axisymmetricflow field needed in the working section from the generally highlyperturbed turbulent and non-axisymmetric flow prevailing in the sheathgas exhaust chamber. Earlier DMA models have sought that isolation byhaving high flow constrictions. We have used much smaller constrictionsforced by the need to minimize pressure drop and maximize flow rate. Ineither case, even if the constriction isolates the mean flow in thesampling slit region from the sheath gas exhaust chamber, pressurefluctuations travel at the speed of sound, and can still propagateupstream against a subsonic flow. Hence, the intense fluctuations surelypresent in the sheath gas exhaust chamber can radiate upstream, therebylimiting resolution. This possibility is potentially most damaging atflow conditions able to excite acoustic resonances either in the exhaustchamber or the working section of the DMA. Such resonances have beenobserved in the Herrmann DMA described earlier in the vicinity of acritical Reynolds number, and lead to a serious deterioration of theinstrument's resolution in a relatively wide range of flow rates aboutthe critical. If the resonance is created within the exhaust chamber,its negative effects in the working section would be specially seriousin low pressure drop designs due to their relatively small constriction.This acoustic radiation phenomenon has not been studied to any extent inDMAs, probably because it is not sufficiently intense to modifyresolution under typical operating conditions, where ΔZ/Z is as high as10 or 20%. Furthermore, typical DMA Reynolds numbers are small andassociated acoustic noise in the exhaust chamber must be modest.

[0088] However, the very large Reynolds numbers of interest to thisinvention lead to substantially more intense acoustic fields, which canbe heard very well, even when no resonance seems to be excited. The needfor resolutions in the vicinity of 1% also makes the impact of smallradiative effects potentially serious. This is a common problem in manyflow systems, and can be alleviated by a variety of means, includinggeometrical and fluid dynamical design. In addition to these traditionalschemes, the present invention includes the possibility to isolatecompletely the laminar working section from the acoustic radiation fieldfrom the inevitably turbulent sheath gas exhaust chamber by driving theflow to sonic conditions at the throat following the aerosol samplingslit.

[0089] Another embodiment of the present invention would use a highspeed subsonic flow through the whole analyzing region including amoderate distance downstream the aerosol sampling slit. The flow wouldthen be accelerated to sonic and slightly supersonic conditions throughthe nozzle throat and beyond it, and the supersonic region would isolatethe working region of the. DMA from acoustic radiation from the highlyperturbed flow present further downstream. A slight contraction willmake the flow sonic in the throat and slightly supersonic thereafter,precluding completely the entry of any pressure fluctuations fromdownstream the throat into the sensitive analyzing section.

What is claimed:
 1. A method of separating charged particles or ions ina differential mobility analyzer, wherein a stream of charged particlesor ions is introduced into an upstream portion of an analyzing regionthrough an inlet slit or orifice and wherein a combination of a laminarflow field and an electrical field leads to ions of different mobilitiesseparating in space, said method comprising the steps of: (a)introducing a stream of charged particles or ions of various electricalmobilities into said analyzing region; (b) laminarizing a flow of anion-free sheath gas, and introducing said sheath gas into saiddifferential mobility analyzer immediately upstream of said analyzingregion; (c) maintaining the flow of said sheath gas within saidanalyzing region as laminar flow; (d) providing an electrical field insaid analyzing region by a combination of electrodes and grids chargedto various voltages, and charging devices to maintain said electrodesand grids at said various voltages; and (e) sampling or collecting saidseparated particles or ions within a narrow range of electricalmobilities through at least one sampling or collector device, the lastof which defines the exit of said analyzing region.
 2. A methodaccording to claim 1, wherein maintaining said flow of said sheath gasas a laminar flow comprises a gradual reduction of the flowcross-section as the sheath gas moves downstream through said analyzingregion.
 3. A method according to claim 1, wherein maintaining said flowof said sheath gas as a laminar flow in an entry region where it meetssaid inlet stream of ions comprises reducing a cross section of saidflow in said entry region to locally accelerate said flow.
 4. A methodaccording to claim 1, wherein said laminar flow is accelerated to avelocity above 100 m/s within said analyzing region.
 5. A methodaccording to claim 4, wherein said velocity of said laminar flow in saidanalyzing region is increased above 100 m/s by introducing a flowconstriction or throat downstream of the exit of said analyzing region,while using a flow channel area at this throat of at least one half ofits value at the exit of said analyzing region.
 6. A method according toclaim 5, wherein said throat is followed by a diverging diffuser.
 7. Amethod according to claim 5, wherein said throat is followed by anexhaust chamber connected to at least three symmetrically distributedexhaust lines.
 8. A method according to claim 5, wherein said velocityof said laminar flow is increased by supporting one or more of saidelectrodes or grids upstream of said analyzing region.
 9. A methodaccording to claim 1, wherein said stream of charged particles or ionsis produced by ionizing preexisting volatile substances upstream of saidinlet slit.
 10. A method according to claim 9, wherein said particles orions are charged with a radioactive source.
 11. A method according toclaim 10, wherein said radioactive source is selected from the groupconsisting of ⁶³Ni, ²¹⁰Po, and other alpha and beta emitters.
 12. Amethod according to claim 9, wherein said particles or ions are chargedusing electrospraying.
 13. A method according to claim 6, wherein saidanalyzing region is isolated from downstream acoustic radiation bycausing flow in a region between the at least one sampling or collectordevice and said diffuser to reach the speed of sound.
 14. A methodaccording to claim 1, where at least two of said electrodes or grids areaxisymmetric within said analyzing region, with geometrical errorssmaller than 0.5% of the smallest distance encountered in said analyzingregion between said at least two electrodes or grids.
 15. A methodaccording to claim 14, where at least two of said electrodes or gridsare axisymmetric within said analyzing region, with geometrical errorssmaller than 0.25% of the smallest distance encountered in saidanalyzing region between said at least two electrodes or grids.
 16. Amethod according to claim 1, wherein resolution of said differentialmobility analyzer is increased by designing an aerosol injection chamberupstream of said inlet slit such that pressure drop for the flow of saidstream of charged particles or ions along a length of the inlet slit issubstantially smaller than for its flow across the inlet slit.
 17. Adifferential mobility analyzer for separating ions and charged particlessuspended in a mixture comprising: means to provide a laminar flow ofion-free sheath gas into an upstream end of an analyzing region at aReynolds number in excess of 2000; ion supply means for introducing saidions and charged particles into said analyzing region; at least twoelectrodes charged to suitable potentials to create an electric fieldwithin said analyzing region; whereby said ions are separated in spaceby combined action of the electric field and the flow of sheath gas; atleast one sampling or collecting device, wherein ions of a desiredmobility are sampled or collected; power supply means to charge said atleast two electrodes to said potentials; means for maintaining saidlaminar flow within said analyzing region; and means to maintain flowspatial symmetry in the analyzing region while minimizing pressure drop.18. The differential mobility analyzer as recited in claim 17, whereinthe ion supply means for introducing said ions and charged particlesinto said analyzing chamber comprise an inlet chamber (12),communicating with the analyzing region via an inlet slit or orifice(4).
 19. The differential mobility analyzer as recited in 18, wherein adownstream end of the means to provide a laminar flow of ion-free sheathgas into the upstream end of the analyzing region is converging until itmeets said inlet slit or orifice (4).
 20. The differential mobilityanalyzer of claim 18, wherein said means for maintaining said laminarflow within said analyzing region comprise a gradual reduction of flowcross section as said flow moves downstream through the analyzingregion.
 21. The differential mobility analyzer of claim 18, wherein saidmeans for maintaining said laminar flow within said analyzing regionincludes means of local acceleration of said flow in an entry region ofsaid analyzing region at a point where said particle-free sheath gasmeets said inlet stream of particles or ions.
 22. The differentialmobility analyzer of claim 21, wherein said means of local accelerationcomprise reducing the cross section of the flow.
 23. The differentialmobility analyzer of claim 18, wherein the means to maintain flowspatial symmetry in the analyzing region while minimizing pressure dropcomprises use of a throat downstream from last of said at least onesampling or collecting device.
 24. The differential mobility analyzer ofclaim 23, further comprising an exhaust chamber downstream of throat.25. The differential mobility analyzer of claim 24, wherein the exhaustchamber is connected to a downstream pumping chamber through at leasttwo symmetrically placed exhaust tubes.
 26. The differential mobilityanalyzer of claim 17, wherein velocity of said laminar flow in a leastone point of said analyzing chamber exceeds 100 m/s.
 27. Thedifferential mobility analyzer as recited in claim 18, wherein the meansto maintain flow spatial symmetry in the analyzing region whileminimizing pressure drop comprises supporting at least one of said atleast two electrodes upstream from the analyzing region.
 28. Thedifferential mobility analyzer as recited in claim 18, wherein one ofsaid at least two electrodes has its leading edge downstream of saidinlet slit so as to minimize diffusion broadening.
 29. The differentialmobility analyzer as recited in claim 18, wherein the means to provide alaminar flow of ion-free sheath gas into the upstream end of ananalyzing region comprise passing said sheath gas through at least onefilter and at least one screen, and then accelerating it through aconverging region.
 30. The differential mobility analyzer as recited inclaim 29, wherein the screen most downstream among said at least onescreen makes the flow turbulent by operating above a critical Reynoldsnumber necessary to produce screen turbulence, and wherein thisturbulent flow is subsequently relaminarized in said converging region.31. The differential mobility analyzer of claim 17, wherein said streamof charged particles or ions is produced by ionizing preexistingvolatile substances in a space located upstream of said inlet slit bysuitable charging means.
 32. The differential mobility analyzer of claim31, wherein said charging means comprise a radioactive source.
 33. Thedifferential mobility analyzer of claim 32, wherein said radioactivesource is selected from the group consisting of ⁶³Ni, ²¹⁰Po and otheralpha or beta emitters.
 34. The differential mobility analyzer of claim33, wherein said charging means comprises an electrospray source. 35.The differential mobility analyzer of claim 17, wherein said analyzingregion is isolated from downstream acoustic radiation by causing theflow to reach the speed of sound in a region between said at least onecollector device and a diffuser.
 36. The differential mobility analyzerof claim 17, wherein at least two of said electrodes or grids areaxisymmetric within said analyzing region, with geometrical errorssmaller than 0.5% of the smallest distance encountered in said analyzingregion between said at least two electrodes or grids.
 37. Thedifferential mobility analyzer of claim 35, wherein at least two of saidelectrodes or grids are axisymmetric within said analyzing region, withgeometrical errors smaller than 0.25% of the smallest distanceencountered in said analyzing region between said at least twoelectrodes or grids.
 38. The differential mobility analyzer of claim 17,wherein resolution is increased by designing an aerosol injectionchamber upstream of said inlet slit such that pressure drop for the flowof said stream of charged particles or ions along a length of the inletslit is substantially smaller than for its flow across the inlet slit.